I have been keeping fish since before I was in grade school, so I have made a TON of mistakes that were easily avoidable.
Rule #1: As almost everyone has mentioned, be patient. Don't go buy a tank today and stock it to the brim tomorrow. You'll just be wasting time and money. Lots and lots of money. (This is a lesson I am just now grasping and I've been doing this for a very long time...)
Rule #2: Buy the biggest freakin' tank you can handle. Don't go buy a 10 gallon tank thinking "I'll get a bigger one once I learn a little more". Learn a little more now, and spring for the biggest thing you can fit into your budget (and your home). Granted, if you just have the budget and space for a ten gallon, then that is the tank for you, but go larger if you can. They're easier to keep clean and regulated, plus, you have more options fish-wise if you have at least 30 gallons to deal with.
Rule #3: Do your homework and buy something you can take care of. If you walk into a fish store and buy something based on looks alone, you are most likely setting yourself up for disaster. There are tons of fish dealers that will give you the BS story about how fish only grow as large as their environment (which is true in a way, they'll die when they run out of room), or that the fish will only become aggressive when you start feeding it live food.... all the stories that are designed to talk you into buying something that will in all likelihood die within a short timeframe (and since you fell in love with the fish, you'll buy another just like it and start the cycle all over again). Be aware of any animal's habits, adult size, agressiveness, diet requirements, etc., so that you don't make this mistake when you walk in the door and get mowed over by a salesperson. (case in point, I purchased a redfin barracuda and took it home to my 55 gallon tank, at which point it proceeded to eat everything in my tank and then run into the walls because it didn't have room, eventually running itself into a heart attack....I didn't do my research until after the fish died and I was out $75. The silly fish needed at least six feet of running room and virtually no other tankmates....)
Rule #4: Don't fill your tank with fish. Never follow that 1" to a gallon BS. There are very, very few fish species that can live in conditions that crowded. You wouldn't have 15 full-grown Rottweillers in your backyard just because someone told you they only need 5 square feet of area to live, right? Use common sense, and don't try to stuff as many fish in your home tank as the lfs has in his. Keep in mind, the fish dealer has the fish in there to get rid of them, not to keep them as pets....and chances are, his tanks are not as healthy as you would want your home tank to be.....(the exception to this is my lfs, the owner makes sure the fish are in very good living conditions and treats them like pets, not like stock to be sold....He does slightly overcrowd them a couple days a week when new shipments come in, however....)
Rule #5: If you have a problem, don't be afraid to ask questions. This is a great forum for beginners, and we've all experienced some kind of tragic loss or another, so don't leave yourself in the dark, and don't give up, thinking that some people just aren't good with fish. It takes a lifetime to learn everything there is to know, and even the experts ask questions every now and again. You're not alone, so ask away, even if the question you have seems trivial. These folks are here to help.
It is a truly great hobby to keep any kind of pet, and fish offer so many great things to someone who is willing to learn. Never give up, and great rewards await you once you've got the basics down.
Pinball Queen, lenghty-posting knowitall....